Main Analysis (All Data)
First, the GLMM model was fit with a full random effects structure.
full.hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH*PDE*Agent|ID) + (1+Agent|dilemma), data=df, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
This returned a singularity issue. Therefore, the complexity of the random effects structure was reduced (by order of importance) until no singularity warning was returned. The model below was the final fitted model.
hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH+PDE|ID) + (1|Dilemma), data=df, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
#OR coefficients
OR_hVai <- exp(fixef(hVai))
#CIs
ci_hVai <- confint(hVai, method = "Wald")
ci_hVai.or <- exp(ci_hVai)
ses_hVai <- sqrt(diag(vcov(hVai)))
Table 1. Logistic GLMM Human v AI MJs explained by MG (OR)
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Table 2. Logistic GLMM Human v AI MJs explained by MG (Log Odds) |
Main Effects Plots
Interaction Effects Plots
Simple Effects Analysis of Main Model (by factor)
Estimated Marginal Means
Table 3. Estimated marginal means by PBH × PDE within Agent
Table 4. Estimated marginal means by PDE x Agent within PBH
Table 5. Estimated marginal means by Agent × PDE within PDE
Contrasts of EMMs
Table 8. Pairwise contrasts for PDE within PBH
[1] “
”
Table 6. Pairwise contrasts for PBH × PDE within Agent
Table 7. Pairwise contrasts for PDE × Agent within PBH
Table 8. Pairwise contrasts for PBH × Agent within PDE
Two Sided Equivalence Test for Main Analysis
Table 9. TOST-test for Practical Equivalence for Main Model
Figure 9.
TOST results for Main
Analysis
Note. Bounds set to mid-point value of small effect size boundary for log odds (±0.94). This is what the study was actually powered to detect for a three-way interaction.
Model Comparisons
Table 10. Comparison of logistic GLMMs with alternative fixed-factor combinations predicting moral judgments (with RE structure as in final model)
Note. Lower AIC and BIC indicate better fit.
Model Checks
Removing dilemmas with ambiguous MG predictions
The additional dilemmas developed in-lab did not have explicit predictions in the MG model. For the most part, these could be estimated based off of the predictions made for alternative dilemmas, and/or guided by the fulfilments of PBH/PDE. However, the unprohibited better alternative equipment-only disproportionate cost intended and the unprohibited better alternative disproportionate cost scenarios had particularly ambiguous estimates. Therefore, for the first study and this study, I conduct analyses with, and without, these dilemmas. Until, at least there is sufficient information available to provide more appropriate predictions.
First, the GLMM model was fit with a full random effects structure.
full.hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH*PDE*Agent|ID) + (1+Agent|dilemma), data=reduced_df, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
This returned a singularity issue. Therefore, the complexity of the random effects structure was reduced (by order of importance) until no singularity warning was returned. The model below was the final fitted model.
hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH+PDE+Agent|ID) + (1|Dilemma), data=reduced_df, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
This model returned no singularity error but the correlations between the RE slopes and the intercept were very high (0.82-0.95), suggesting overfitting. Therefore, the random effects structure was further reduced by removing the random slope for Agent. This returned no singularity warning and much lower correlations between the RE slopes and intercept.
hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH+PDE|ID) + (1|Dilemma), data=reduced_df, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
#OR coefficients
OR_hVai <- exp(fixef(hVai))
#CIs
ci_hVai <- confint(hVai, method = "Wald")
ci_hVai.or <- exp(ci_hVai)
ses_hVai <- sqrt(diag(vcov(hVai)))
Table 2. Logistic GLMM Human v AI MJs explained by MG (OR)
|
Table 1. Logistic GLMM Human v AI MJs explained by MG (Log Odds) |
Main Effects Plots
Interaction Effects Plots
Simple Effects Analysis of Main Model (by factor)
Estimated Marginal Means
Table 5. Estimated marginal means by PDE within PBH
Table 3. Estimated marginal means by PBH × PDE within Agent
Table 4. Estimated marginal means by PDE x Agent within PBH
Table 5. Estimated marginal means by Agent × PBH within PDE
Contrasts of EMMs
Table 8. Pairwise contrasts for PDE within PBH
Table 6. Pairwise contrasts for PBH × PDE within Agent
Table 7. Pairwise contrasts for PDE × Agent within PBH
Table 8. Pairwise contrasts for PBH × Agent within PDE
Two Sided Equivalence Test for Main Analysis (Reduced Dilemmas)
Table 9. TOST-test for Practical Equivalence for Model with Reduced Dilemmas
Figure 9.
TOST results for
Analysis of Model with Reduced Dilemmas
Note. Bounds set to mid-point value of small effect size boundary for log odds (±0.94). This is what the study was actually powered to detect for a three-way interaction.
Model Comparisons
Table 10. Comparison of logistic GLMMs with alternative fixed-factor combinations predicting moral judgments (with RE structure as in final model)
Note. Lower AIC and BIC indicate better fit.
Model Checks
Removing Participants who failed a costless rescue Human scenario
First, the GLMM model was fit with a match random effects structure.
full.hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH*PDE*Agent|ID) + (1+Agent|dilemma), data=df_match, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
This returned a singularity issue. Therefore, the complexity of the random effects structure was match (by order of importance) until no singularity warning was returned. The model below was the final fitted model.
hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH+PDE|ID) + (1|Dilemma), data=df_match, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
#OR coefficients
OR_hVai <- exp(fixef(hVai))
#CIs
ci_hVai <- confint(hVai, method = "Wald")
ci_hVai.or <- exp(ci_hVai)
ses_hVai <- sqrt(diag(vcov(hVai)))
Table 2. Logistic GLMM Human v AI MJs explained by MG (OR)
|
Table 1. Logistic GLMM Human v AI MJs explained by MG (Log Odds) |
Main Effects Plots
Interaction Effects Plots
Simple Effects Analysis of Main Model (by factor)
Estimated Marginal Means
Table 5. Estimated marginal means by PDE within PBH
Table 3. Estimated marginal means by PBH × PDE within Agent
Table 4. Estimated marginal means by PDE x Agent within PBH
Table 5. Estimated marginal means by Agent × PBH within PDE
Contrasts of EMMs
Table 7. Pairwise contrasts for PDE within PBH
Table 6. Pairwise contrasts for PBH × PDE within Agent
Table 7. Pairwise contrasts for PDE × Agent within PBH
Table 8. Pairwise contrasts for PBH × Agent within PDE
Two Sided Equivalence Test for Main Analysis
Table 9. TOST-test for Practical Equivalence for Main Model
Figure 9.
TOST results for Main
Analysis
Note. Bounds set to mid-point value of small effect size boundary for log odds (±0.94). This is what the study was actually powered to detect for a three-way interaction.
Model Comparisons
Table 10. Comparison of logistic GLMMs with alternative fixed-factor combinations predicting moral judgments (with RE structure as in final model)
Note. Lower AIC and BIC indicate better fit.
Model Checks
Removing Participants who failed CR Human scenario and dilemmas with ambiguous MG predictions.
First, the GLMM model was fit with a reduced_match random effects structure.
full.hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH*PDE*Agent|ID) + (1+Agent|dilemma), data=reduced_df_match, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
This returned a singularity issue. Therefore, the complexity of the random effects structure was reduced_match (by order of importance) until no singularity warning was returned. The model below was the final fitted model.
hVai <- glmer(MJ ~ PBH*PDE*Agent + (1+PBH+PDE|ID) + (1|Dilemma), data=reduced_df_match, family = binomial(link = "logit"),
control = glmerControl(optCtrl = list(maxfun = 2e5), optimizer = "bobyqa"))
#OR coefficients
OR_hVai <- exp(fixef(hVai))
#CIs
ci_hVai <- confint(hVai, method = "Wald")
ci_hVai.or <- exp(ci_hVai)
ses_hVai <- sqrt(diag(vcov(hVai)))
Table 2. Logistic GLMM Human v AI MJs explained by MG (OR)
|
Table 1. Logistic GLMM Human v AI MJs explained by MG (Log Odds) |
Main Effects Plots
Interaction Effects Plots
Simple Effects Analysis of Main Model (by factor)
Estimated Marginal Means
Table 5. Estimated marginal means by PDE within PBH
Table 3. Estimated marginal means by PBH × PDE within Agent
Table 4. Estimated marginal means by PDE x Agent within PBH
Table 5. Estimated marginal means by PBH within PDE
Contrasts of EMMs
Table 7. Pairwise contrasts for PDE within PBH
Table 6. Pairwise contrasts for PBH × PDE within Agent
Table 7. Pairwise contrasts for PDE × Agent within PBH
Table 8. Pairwise contrasts for PBH × Agent within PDE
Two Sided Equivalence Test for Main Analysis
Table 9. TOST-test for Practical Equivalence for Main Model
Figure 9.
TOST results for Main
Analysis
Note. Bounds set to mid-point value of small effect size boundary for log odds (±0.94). This is what the study was actually powered to detect for a three-way interaction.
Model Comparisons
Table 10. Comparison of logistic GLMMs with alternative fixed-factor combinations predicting moral judgments (with RE structure as in final model)
Note. Lower AIC and BIC indicate better fit.